Andrea Boston, the co-author of the study and senior public health advisor, says the development is "unfortunate".
As many convenience stores are located in residential neighbourhoods near schools, she says this could lead to an increase in young people vaping.
"If this trend continues, we could see more rangatahi exposed to vape stores and promotional signage in their neighbourhood. We are concerned this exposure could further normalise vaping for young people," Boston said.
She added it may be difficult for convenience store staff to enforce the age requirements in the store, as often there is just one person working.
There needs to be more controls in place to stop shops creating vaping stores inside their premises says Boston.
"We need to balance providing people who smoke with a reduced harm alternative while also protecting people who do not smoke from exposure to products and promotions that encourage vaping experimentation."
The research suggests the current regulations may need to be strengthened, and that vaping products should only be sold in specialist stores. The density of these stores should be limited too, and locations should be considered to ensure people who have never smoked do not take up vaping.